When the sequence a, b, c, ... is geometric, the shift operation s is exactly the same as multiplying by r, so we get back to the previous result: the nth polynomial is then a(x + r)^n. Otherwise, though, and in general, we have the [(x + s)^n]a form, which is almost as nice.
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Laurens ... I somehow missed your whole sequence of tweets here and saw only the first one! Now parsing!
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It's an interesting body of algebraic lore here, James, which I think you'll find is worth pondering. It ought, I think, to be better known, and, when followed to its logically natural limits, it leads to some fascinating things.
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@threadreaderapp God wants polynomials written a certain way, and I suspect he'd also like you to unroll the thread. -
I'm embarrassed never to have learned how to do this. I suppose I'd better amend that situation.
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